Outcome: N8.3

Demonstrate understanding of rates, ratios, and proportional reasoning concretely, pictorially, and symbolically.

Indicators:

·  Identify and explain ratios and rates in familiar situations (e.g., cost per music download, traditional mixtures for bleaching, time for a hand-sized piece of fungus to burn, mixing of colours, number of boys to girls at a school dance, rates of traveling such as car, skidoo, motor boat or canoe, fishing nets and expected catches, or number of animals hunted and number of people to feed).

·  Identify situations (such as providing for the family or community through hunting) in which a given quantity of a/b represents a:

o  fraction

o  rate

o  quotient

o  percent

o  probability

o  ratio.

·  Demonstrate (orally, through arts, concretely, pictorially, symbolically, and/or physically) the difference between ratios and rates.

·  Verify or contradict proposed relationships between the different roles for quantities that can be expressed in the form a/b. For example:

o  a rate cannot be represented by a percent because a rate compares two different types of measurements while a percent compares two measurements of the same type

o  probabilities cannot be used to represent ratios because probabilities describe a part to whole relationship but ratios describe a part to part relationship

o  a fraction is not a ratio because a fraction represents part to whole

o  a ratio cannot be written as a fraction, unless the quantity of the whole is first determined (e.g., 2 parts white and 5 parts red paint is 2/7 white)

o  a ratio cannot be written as percent unless the quantity of the whole is first determined (e.g., a ratio of 4 parts blue and 6 parts red paint can be described as having 40% blue).

·  Write the symbolic form (e.g., 3:5 or 3 to 5 as a ratio, $3/min or $3 per one minute as a rate) for a concrete, physical, or pictorial representation of a ratio or rate.

·  Explain how to recognize whether a comparison requires the use of proportional reasoning (ratios or rates) or subtraction.

·  Create and solve problems involving rates, ratios, and/or probabilities.

Level / Scale / Descriptor / Indicators / Student-Friendly Language
Pre-Requisite Knowledge / ·  Students who are not able to be independently successful with level 1 questions will be given an E. / Grade 8 Numeracy Nets
Checkpoint 8 - Students use multiplicative reasoning to solve problems
1 / B - Beginning
There is a partial understanding of some of the simpler details and processes.
Prior knowledge is understood. / ·  Knowledge and Comprehension
·  Students who are successful with level 1 questions or those who are successful with level 1 or 2 questions with assistance will be given a B. / ·  Identify and explain ratios and rates in familiar situations (e.g., cost per music download, traditional mixtures for bleaching, time for a hand-sized piece of fungus to burn, mixing of colours, number of boys to girls at a school dance, rates of traveling such as car, skidoo, motor boat or canoe, fishing nets and expected catches, or number of animals hunted and number of people to feed). / I can think of and discuss examples where ratios and rates are used (the cost of downloading music, the number of boys to girls in our class).
2 / A – Approaching
No major errors or omissions regarding the simpler details or processes, but assistance may be required with the complex processes. / ·  Applying and Analysing
·  Students who are able to be successful with level 1 and level 2 questions, or those who are successful with higher-level questions with assistance, will be given an A. / ·  Identify situations (such as providing for the family or community through hunting) in which a given quantity of a/b represents a:
o  fraction
o  rate
o  quotient
o  percent
o  probability
o  ratio.
·  Demonstrate (orally, through arts, concretely, pictorially, symbolically, and/or physically) the difference between ratios and rates.
·  Write the symbolic form (e.g., 3:5 or 3 to 5 as a ratio, $3/min or $3 per one minute as a rate) for a concrete, physical, or pictorial representation of a ratio or rate. / I can think of situations where a/b represents a fraction, a rate, a quotient, a percent, a probability, or a ratio.
·  2/3 means 2 pieces of a chocolate bar that is cut into 3 pieces
·  2/3 means 2 chocolate bars for every three dollars I spend
·  2/3 means that I got 2 out of 3 or 67% on my mini-quiz
I can demonstrate (using words, pictures or actions) the difference between ratios and rates.
I can write the symbolic representation (1/3, 1:3. 1 to 3) for ratios and rates that are demonstrated using words, pictures or actions.
3 / M – Meeting
No major errors or omissions regarding any of the information and/or processes that were explicitly taught.
This is the target level for proficiency. / ·  Evaluating and Creating
·  Students who are independently successful with level 3 or level 4 questions are given an M. / ·  Explain how to recognize whether a comparison requires the use of proportional reasoning (ratios or rates) or subtraction.
·  Verify or contradict proposed relationships between the different roles for quantities that can be expressed in the form a/b. For example:
o  a rate cannot be represented by a percent because a rate compares two different types of measurements while a percent compares two measurements of the same type
o  probabilities cannot be used to represent ratios because probabilities describe a part to whole relationship but ratios describe a part to part relationship
o  a fraction is not a ratio because a fraction represents part to whole
o  a ratio cannot be written as a fraction, unless the quantity of the whole is first determined (e.g., 2 parts white and 5 parts red paint is 2/7 white)
o  a ratio cannot be written as percent unless the quantity of the whole is first determined (e.g., a ratio of 4 parts blue and 6 parts red paint can be described as having 40% blue).
·  Create and solve problems involving rates, ratios, and/or probabilities. / I can determine whether a comparison is multiplicative (proportional) or additive (the difference is a subtracted amount).
I know whether each of the following is true or false and I can explain the reasons for my choice:
·  a rate cannot be represented by a percent because a rate compares two different types of measurements while a percent compares two measurements of the same type
·  probabilities cannot be used to represent ratios because probabilities describe a part to whole relationship but ratios describe a part to part relationship
·  a fraction is not a ratio because a fraction represents part to whole
·  a ratio cannot be written as a fraction, unless the quantity of the whole is first determined (e.g., 2 parts white and 5 parts red paint is 2/7 white)
·  a ratio cannot be written as percent unless the quantity of the whole is first determined (e.g., a ratio of 4 parts blue and 6 parts red paint can be described as having 40% blue).
I can create and solve problems that involve rates, ratios and/or probabilities.
4 / In addition to level 3 performance, in-depth inferences and applications go beyond what was explicitly taught. / ·  Students successful at level 4 will receive supplementary comments specific to their achievement in addition to the M. / ** This can be anything that you would want the students to move on to when they have met the outcome.

Student-Friendly Rubric

Outcome: N8.3

Demonstrate understanding of rates, ratios, and proportional reasoning concretely, pictorially, and symbolically.

Meeting
Approaching / I can determine whether a comparison is multiplicative (proportional) or additive (the difference is a subtracted amount).
I know whether each of the following is true or false and I can explain the reasons for my choice:
·  a rate cannot be represented by a percent because a rate compares two different types of measurements while a percent compares two measurements of the same type
·  probabilities cannot be used to represent ratios because probabilities describe a part to whole relationship but ratios describe a part to part relationship
·  a fraction is not a ratio because a fraction represents part to whole
·  a ratio cannot be written as a fraction, unless the quantity of the whole is first determined (e.g., 2 parts white and 5 parts red paint is 2/7 white)
·  a ratio cannot be written as percent unless the quantity of the whole is first determined (e.g., a ratio of 4 parts blue and 6 parts red paint can be described as having 40% blue).
I can create and solve problems that involve rates, ratios and/or probabilities.
Beginning / I can think of situations where a/b represents a fraction, a rate, a quotient, a percent, a probability, or a ratio.
·  2/3 means 2 pieces of a chocolate bar that is cut into 3 pieces
·  2/3 means 2 chocolate bars for every three dollars I spend
·  2/3 means that I got 2 out of 3 or 67% on my mini-quiz
I can demonstrate (using words, pictures or actions) the difference between ratios and rates.
I can write the symbolic representation (1/3, 1:3. 1 to 3) for ratios and rates that are demonstrated using words, pictures or actions.
I can think of and discuss examples where ratios and rates are used (the cost of downloading music, the number of boys to girls in our class).